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Preprints, Working Papers, ... Year : 2021

Numerical control of a semilinear wave equation on an interval

Abstract

We are concerned with the numerical exact controllability of the semilinear wave equation on the interval (0, 1). We introduce a Picard iterative scheme yielding a sequence of approximated solutions which converges towards a solution of the null controllability problem, provided that the initial data are small enough. The boundary control, which is applied at the endpoint x = 1, is taken in the space H 1 0 (0,T) for T = 2. For the linear part, the control input is obtained by imposing a transparent boundary condition at x = 1. Next, we provide several simulations to show the efficiency of the algorithm, using collocation pseudospectral methods on Chebychev grids to discretize the second order derivative in space in the wave equation.
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Dates and versions

hal-03369560 , version 1 (07-10-2021)

Identifiers

  • HAL Id : hal-03369560 , version 1

Cite

M M Cavalcanti, V N Domingos Cavalcanti, Carole Rosier, Lionel Rosier. Numerical control of a semilinear wave equation on an interval. 2021. ⟨hal-03369560⟩
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